416. By the 4th Table, find the Expansion of Air, with 27°.36, on Feet 423.67 Tenths.

Section 406.

First, with 27°, on 423.67, thus:

viz. on 400

as 4000 = 262.4

 decimated 26.24

20

as 2000 = 131.2

 1.312

3

as 3000 = 196.8

 .1968

.6

as 6000 = 393.6

 .03936

.07

as 7000 = 459.2

 .004592
—————

Expansion =

 27.692752

Section 407.

Second, with .36 on the same, thus:

on 400

as 4000 = 349.9

 decimated .3499

20

as 2000 = 174.9

 .01749

3

as 3000 = 262.4

 .002624

.6

as 6000 = 524.8

 .0005248

.07

as 7000 = 612.3

 .00006123
—————

Expansion =

 .37050003

Add the former

 27.692752
—————

Height in Feet

 28.06325203

417. Which Height for Expansion of Air, with more than the Standard Heat, being added⁠[133] to the Height, for Expansion of the Barometer, with the Standard-Heat, gives the true Height of the upper Barometer, at the given Heat.

For Expansion of Air above Standard Heat,

Height in Feet

28.0
For Expansion of Barometer,

with Standard: Height in Feet

423.6

———
418. True Height of the upper Barometer

451.6
Lower Barometer 1 Foot above the Water

1.0

Height of the Top of the Cross above the Gallery

50.0

———
Height of the Top of the Cross above the Tyber

502.6
Height of the same, measured the same Day
geometrically, was Feet

502.9

End of the last Stage.